Kerodon

Notation 7.6.6.7. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories and let $\kappa $ be an infinite cardinal. We let $\operatorname{Fun}^{\kappa -\mathrm{cont}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the $\kappa $-continuous functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$, and $\operatorname{Fun}^{\kappa -\mathrm{cocont}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ the full subcategory of $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the $\kappa $-cocontinuous functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.